There are 2 phases to this study. In the first phase, 3 different dose levels of topotecan are being studied. The dose of topotecan that you receive will depend on when you are enrolled. It will also depend on whether or not other participants had side effects from their treatment. Although the dose of topotecan will vary, the dose of gefitinib is the same for all participants. Up to 6 participants may be treated at each dose. The goal of this portion of the study is to find the highest safe dose of this drug combination. Up to 18 patients will be treated on this part of the study.